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Choreography NC.39

From Hristov, Hristova, Puzynin, Puzynina, Sharipov & Tukhliev (2024)

Choreography NC.39 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 129.78 time units, published by Hristov, Hristova, Puzynin, Puzynina, Sharipov & Tukhliev (2024). Choreographies whose knot is not a power of the figure-eight’s: three bodies on one closed curve with a topology of its own. Computed to 180 digits; all unstable. It is unstable (largest Floquet multiplier 188716739), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0282 of each other at a top speed of 6.21, line up 84 times a period, and the computed loop closes to 2.8×10⁻²³.

Measured over one period

Period: 129.7801804
Masses: 1 : 1 : 1
Energy: -0.955800
Angular momentum: 0
Closest approach: 0.02817
Top speed: 6.205
Path length: 253.07
Alignments per period: 84
Topology: aaaBAbAbaBAAbaBaBabABBAbaaBAbbaBAABabAbAbaBBAbaBaBAbbbAB (free-group class)
Stability: unstable (|λ|max 1.9×10⁸, published)
Loop closure: 2.8×10⁻²³

Neighbours on the map

All Nontrivial choreographies, the families of periodic three-body orbits, or the atlas map.